{"id":1076,"date":"2020-06-14T11:00:00","date_gmt":"2020-06-14T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=1076"},"modified":"2020-06-13T10:27:18","modified_gmt":"2020-06-13T01:27:18","slug":"variance","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/variance","title":{"rendered":"\u5206\u6563\u306e\u5b9a\u7fa9\u3010\u78ba\u7387\u5909\u6570\u306e\u5206\u6563\u3092\u77e5\u308b\u3011"},"content":{"rendered":"\n<p class=\"has-text-align-right\"><span style=\"text-decoration: underline;\">\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606<\/span><\/p>\n\n\n\n\n\n\n\n<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u5206\u6563\u3092\u5b9a\u7fa9\u3057\u3066\u3044\u307e\u3059\u3002\u5206\u6563\u306f\u30c7\u30fc\u30bf\u306e\u6563\u3089\u3070\u308a\u5177\u5408\u3092\u8868\u3059\u3082\u306e\u3067\u3059\u3002\u5e73\u5747\u3092\u8868\u3059\u671f\u5f85\u5024\u3068\u5171\u306b\u8003\u3048\u308b\u3053\u3068\u3067\u3001\u305d\u306e\u529b\u3092\u767a\u63ee\u3057\u307e\u3059\u3002\u6761\u4ef6\u4ed8\u304d\u5206\u6563\u304a\u3088\u3073\u5206\u6563\u306e\u6027\u8cea\u306f\u5225\u306e\u8a18\u4e8b\u3067\u7d39\u4ecb\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u8208\u5473\u306e\u3042\u308b\u65b9\u306f\u305d\u3061\u3089\u3082\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<div id=\"toc_container\" class=\"toc_light_blue no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u5206\u6563\u306e\u5b9a\u7fa9<\/a><ul><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_2\">1.1<\/span> \u30b5\u30a4\u30b3\u30ed\u306e\u5834\u5408<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_2\">1.2<\/span> \u30af\u30b8\u5f15\u304d\u306e\u5834\u5408<\/a><\/li><\/ul><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">2<\/span> \u5206\u6563\u306e\u307e\u3068\u3081<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_1\">3<\/span> \u5206\u6563\u306e\u95a2\u9023\u8a18\u4e8b<\/a><\/li><\/ul><\/div>\n<h3><span id=\"i\">\u5206\u6563\u306e\u5b9a\u7fa9<\/span><\/h3>\n\n\n\n<div style=\"display: inline-block; background: #33cc33; padding: 5px 10px; color: #ffffff; border-radius: 5px 5px 0 0;\"><strong>\u5206\u6563(variance)<\/strong><\/div>\n<div style=\"background: #ffffea; padding: 10px; border: 2px solid #33cc33;\">\u78ba\u7387\u5909\u6570\\(X\\)\u306e\u5206\u6563\u306f\u8a18\u53f7\\(\\mathrm{Var}[X]\\)\u3067\u8868\u3057\u3001\\(X\\)\u306e\u671f\u5f85\u5024\\(\\mu\\)\u3092\u7528\u3044\u3066\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\n<div style=\"overflow-x: auto;\">\\begin{align}\n\uff08\u96e2\u6563\u578b\uff09&amp; \\mathrm{Var}[X] = \\mathrm{E}\\left[ (X-\\mu)^{2} \\right] =\\sum_{i}(x_{i}-\\mu)^{2}f(x_{i}) \\\\\n\uff08\u9023\u7d9a\u578b\uff09&amp; \\mathrm{Var}[X] = \\mathrm{E}\\left[ (X-\\mu)^{2} \\right] =\\int_{-\\infty}^{\\infty}(x-\\mu)^{2}f(x)dx\n\\end{align}<\/div>\n\u3053\u3053\u3067\u3001\\(f(x_{i})\\)\u306f\\(X\\)\u306e\u78ba\u7387\u95a2\u6570\u3092\u8868\u3057\u3001\\(f(x)\\)\u306f\\(X\\)\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\n<\/div>\n<p>&nbsp;<\/p>\n\n\n\n<p>\u3000\u5206\u6563\u306e\u5b9a\u7fa9\u304b\u3089\u5909\u5f62\u3059\u308b\u3068\u6b21\u306e\u5f0f\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002$$\\mathrm{Var}[X]=\\mathrm{E}[X^{2}]-\\mathrm{E}[X]^{2}$$\u5206\u6563\u3092\u6c42\u3081\u308b\u3068\u304d\u306b\u306f\u3001\u5b9a\u7fa9\u304b\u3089\u8a08\u7b97\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u30b3\u30c1\u30e9\u306e\u5f0f\u306e\u65b9\u304c\u3088\u304f\u5229\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-liquid-speech-balloon liquid-speech-balloon-wrap liquid-speech-balloon-00  liquid-speech-balloon-short\"><div class=\"liquid-speech-balloon-avatar\"><\/div><div class=\"liquid-speech-balloon-text\" style=\"border-color:#d6ebf8;background-color:#d6ebf8;color:#000000\"><p>\u5177\u4f53\u4f8b\u3067\u5206\u6563\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\uff01<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\n\n\n\n<p><\/p>\n\n\n\n<h4><span id=\"i-2\">\u30b5\u30a4\u30b3\u30ed\u306e\u5834\u5408<\/span><\/h4>\n\n\n\n<p>\u78ba\u7387\u5909\u6570\u3068\u78ba\u7387\u3092\u307e\u3068\u3081\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter\"><table><tbody><tr><td>\u78ba\u7387\u5909\u6570\\(X\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(1\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(2\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(3\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(4\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(5\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(6\\)<\/td><\/tr><tr><td>\u78ba\u7387\\(\\mathrm{P}(X)\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition\">\uff1c\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\u306e\u8a18\u4e8b\uff1e<\/a>\u3088\u308a\u671f\u5f85\u5024\\(\\mu\\)\u306f\\(\\mu=3.5\\)\u3068\u306a\u308a\u307e\u3059\u3002<br>\u3053\u306e\u3053\u3068\u3092\u7528\u3044\u308b\u3068\u3001\u6c42\u3081\u305f\u3044\u5206\u6563\\(\\sigma^{2}\\)\u306f$$\\sigma^{2}=\\frac{1}{6}\\cdot(1-3.5)^{2}+\\cdots+\\frac{1}{6}\\cdot(6-3.5)^{2}\\approx 2.92$$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b5\u30a4\u30b3\u30ed\u306e\u3088\u3046\u306b\u3001<strong>\u3059\u3079\u3066\u306e\u51fa\u76ee\u306e\u78ba\u7387\u304c\u7b49\u3057\u3044\u5834\u5408\u3001\u30b5\u30a4\u30b3\u30ed\u306e\u5206\u6563\u306f\u30c7\u30fc\u30bf\u306e\u5206\u6563\uff08<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/05241628\">\uff1c\u5206\u6563\u30fb\u6a19\u6e96\u504f\u5dee\u306e\u8a18\u4e8b\uff1e<\/a>\u3092\u53c2\u7167\uff09\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002<\/strong><\/p>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h4><span id=\"i-3\">\u30af\u30b8\u5f15\u304d\u306e\u5834\u5408<\/span><\/h4>\n\n\n\n<p>\u3042\u308b\u30af\u30b8\u5f15\u304d\u306e\u5185\u8a33\u304c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>\u8cb0\u3048\u308b\u91d1\u984d\uff08\u5186\uff09<\/td><td>20<\/td><td>100<\/td><td>500<\/td><td>1500<\/td><td><\/td><\/tr><tr><td>\u304f\u3058\u306e\u672c\u6570\uff08\u672c\uff09<\/td><td>500<\/td><td>300<\/td><td>150<\/td><td>50<\/td><td>\uff08\u5408\u8a08\uff091000\u672c<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition\">\uff1c\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\u306e\u8a18\u4e8b\uff1e<\/a>\u3088\u308a\u671f\u5f85\u5024\\(\\mu\\)\u306f\\(\\mu=190\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u3092\u7528\u3044\u3066\u3001\u3082\u3089\u3048\u308b\u91d1\u984d\u306e\u5206\u6563\\(\\sigma^{2}\\)\u306f$$\\sigma^{2}=\\frac{10}{20}(20-190)^{2}+\\cdots+\\frac{1}{20}(1500-190)^{2}\\approx (342.2)^{2}$$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3><span id=\"i-4\">\u5206\u6563\u306e\u307e\u3068\u3081<\/span><\/h3>\n\n\n\n<p>\u5206\u6563\u306f\u78ba\u7387\u5909\u6570\u306e\u6563\u3089\u3070\u308a\u5177\u5408\u3092\u8868\u3057\u307e\u3059\u3002\u3082\u3046\u5c11\u3057\u8a73\u3057\u304f\u8aac\u660e\u3059\u308b\u3068\u3001\u5206\u6563\u306f\u78ba\u7387\u5909\u6570\u3068\u671f\u5f85\u5024\u306e\u5dee\u30922\u4e57\u3057\u305f\u3082\u306e\u306b\u3001\u78ba\u7387\u3067\u91cd\u307f\u3092\u3064\u3051\u305f\u91cd\u307f\u4ed8\u304d\u7b97\u8853\u5e73\u5747\u3068\u306a\u308a\u307e\u3059\u3002\u78ba\u7387\u5206\u5e03\u306e\u6563\u3089\u3070\u308a\u3092\u8868\u3059\u6307\u6a19\u306b\u306a\u308b\u306e\u3067\u3001\u7d71\u8a08\u7684\u63a8\u6e2c\u3092\u884c\u3046\u4e0a\u3067\u3001\u63a8\u5b9a\u7cbe\u5ea6\u3092\u8868\u3057\u305f\u308a\u3059\u308b\u969b\u306b\u3068\u3066\u3082\u91cd\u8981\u306a\u60c5\u5831\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3><span id=\"i-5\">\u5206\u6563\u306e\u95a2\u9023\u8a18\u4e8b<\/span><\/h3>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/conditional-variance\">\u6761\u4ef6\u4ed8\u304d\u5206\u6563<\/a>\uff1a\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u5909\u6570\u306e\u5206\u6563\u306e\u6c42\u3081\u65b9\u3092\u7d39\u4ecb\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/covariance\">\u5171\u5206\u6563<\/a>\uff1a\u5171\u5206\u6563\u3092\u5b9a\u7fa9\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/variance-nature\">\u5206\u6563\u306e\u6027\u8cea<\/a>\uff1a\u5206\u6563\u306e\u6301\u3064\u6027\u8cea\u3092\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606 \u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u5206\u6563\u3092\u5b9a\u7fa9\u3057\u3066\u3044\u307e\u3059\u3002\u5206\u6563\u306f\u30c7\u30fc\u30bf\u306e\u6563\u3089\u3070\u308a\u5177\u5408\u3092\u8868\u3059\u3082\u306e\u3067\u3059\u3002\u5e73\u5747\u3092\u8868\u3059\u671f &#8230; <\/p>\n","protected":false},"author":1,"featured_media":829,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[74],"tags":[31],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/05\/135-money-images.jpg","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1076"}],"collection":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/comments?post=1076"}],"version-history":[{"count":11,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1076\/revisions"}],"predecessor-version":[{"id":1155,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1076\/revisions\/1155"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/829"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=1076"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=1076"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=1076"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}